A284708 Smallest initial prime p for at least n primes in increasing arithmetic progression with a common difference less than p.
2, 2, 3, 11, 37, 107, 409, 409, 409, 25471, 53173, 65003, 766439, 11797483
Offset: 1
Examples
Smallest initial prime p, primes in arithmetic progression: a(1) = 2: (2); a(2) = 2: (2, 3); a(3) = 3: (3, 5, 7); a(4) = 11: (11, 17, 23, 29); a(5) = 37: (37, 67, 97, 127, 157); a(6) = 107: (107, 137, 167, 197, 227, 257); a(7) = 409: (409, 619, 829, 1039, 1249, 1459, 1669); a(8) = 409: (409, 619, 829, 1039, 1249, 1459, 1669, 1879); a(9) = 409: (409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089);
References
- David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, entry 11410337850553, page 191.
Programs
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PARI
isokd(p, n, d) = for (i=1, n, if (!isprime(p+(i-1)*d), return(0))); 1; isokp(p, n) = for (d=1, p-1, if (isokd(p, n, d), return(1));); a(n) = my(p=2); while (!isokp(p, n), p=nextprime(p+1)); p; \\ Michel Marcus, Mar 15 2023
Extensions
Name edited by Bernard Schott, Mar 15 2023
Comments